Websites for published authors are becoming more and more important, not just for your readers but for the future of your career. I can’t tell you how many times I go to an author’s website to check out not just the author’s books and career but for quotes and reviews. Which is why it’s important to keep your site updated as much as possible. If you have a section for reviews but nothing is there, it looks like you’ve gotten no good reviews.
I know how hard it is to keep up a website, I know that there are plenty of things I’ve missed when I don’t update enough, which is why, over time, I’ve simply removed those sections from my site. If you find you can’t blog regularly or haven’t blogged in months, then simply take down your blog. I think it looks better not to have one than to have a neglected one. The same holds true of reviews. If you can’t remember to get in there once a month and update those sections, then simply remove them.